The agency receives more than 200,000 complaints a month about the prerecorded messages, which offer everything from credit cards to new medications.

"All of us have heard this [robocalls] so many times that it's like nails on a chalkboard for us," says David Vladeck, director of the FTC's Bureau of Consumer Protection.

Vladeck has been going after robocalls for a long time but says the hunt has become much more difficult in recent years.

"These calls are not like the calls we grew up with," he says. "They are computer-blasted calls that are enabled by the Internet. The dialers are outside the U.S. generally, and these dialers are capable of blasting out an unfathomable number of telephone calls."

Last year, the FTC shut down one serial dialer called Asia Pacific, which, in an 18-month period, made more than 2.5 billion robocalls in the U.S.

The majority of telephone calls that deliver prerecorded messages trying to sell you something are illegal — and Vladeck says they're not just annoying, they're dangerous.

"Most of the robocalls we see are for scams that prey on people who are economically vulnerable," he says.

The FTC goes after and sues dozens of robocall companies every year, but Vladeck admits the effort is not enough. Voice over Internet Protocol, VoIP, has offered robocallers a cheap way to reach tens of millions of American consumers and stay offshore.

So, the FTC is challenging innovators to find a solution. It's offering $50,000 to the individual or small company that presents the technology that will enable consumers or telecoms to block the assault of unwanted robocalls.

The agency has already received more than 200 submissions, one of which is from Shawn Davis, an IT technician in Boise, Idaho.

His solution to the robocall problem is called Roboblock 12. It's a number verification system that requires callers to type in randomly generated numbers.

"If they do find a way to get through, and you find out it's an automated solicitor, you just press star-6-6, which is 'no,' and it adds them to the block list," Davis explains.

Many of the submissions use technology to differentiate robots from humans — like those garbled numbers you have to decipher and type in online to prove you're human. But some are less technical.

"Turn your phone off or unplug it," says Naomi Walls of Aurora, Colo. Her submission includes turning your ringer off and recording a message similar to this one: "You have reached the Walls residence. Due to the number of robocalls I'm receiving, I've turned off my phone so that it won't ring."

"That's a good solution for a lot of problems in life," Kara Swisher says with a laugh. She's the co-editor of the All Things Digital website and one of the judges for the robocall competition.

Swisher won't reveal which ideas she likes so far but says the winner could receive more than just money.

"The people who invest in technology pay attention to all these incubators, all these competitions, all these hack-a-thons, so if there's an excellent solution, someone's going to pick it up," Swisher says.